Topological Phase transitions and Topological phases of matter by Reichmann Alexander

Overview Phase transitions Topology Quantum Hall effect Superconductivity Applications

Phase transition Different propteries of materials originate from the different ways in which the atoms are organized Organizations of atoms are called „orders“ Landau symmetry-breaking theory

Topology Topology is a branch of mathematics that describes properties that only change step-wise (in whole numbers). Example of a topological invariant: number of holes

Superconductivity Zero electrical resistance below cricital temperature Above Tc: vortices and antivorices are plentiful and spins are disordered. Below Tc: Vortex-Antivortex pairs are formed below critical temperature

QM Hall effect Classical: QM: Induced voltage in a Conductor is confined Current carrying conductor to two dimensions and Exposed to a magnetic field is cooled to near 0K

Applications: Stanene Tin atoms arranged in a single hexagonal layer Predicted to be a 2D topological insulator Superconductivity at room temperature on its edges